Operators acting on certain Banach spaces of analytic functions

K. Seddighi, K. Hedayatiyan and B. Yousefi

International Journal of Mathematics and Mathematical Sciences, 1995, vol. 18, 1-4

Abstract:

Let 𝒳 be reflexive Banach space of functions analytic plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that 𝒳 contains the constants and M z multiplication by the independent variable z , is bounded operator on 𝒳 . We give sufficient conditions for M z to be reflexive. In particular, we prove that the operators M z on E P ( Ω ) and certain H a P ( β ) reflexive. We also prove that the algebra of multiplication operators on Bergman spaces is reflexive, giving simpler proof of result of Eschmeier.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:796357

DOI: 10.1155/S0161171295000147

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